diff --git a/swh/core/api/__init__.py b/swh/core/api/__init__.py
--- a/swh/core/api/__init__.py
+++ b/swh/core/api/__init__.py
@@ -429,10 +429,9 @@
     on the client side.
 
     """
-    logging.exception(exception)
-
     status_class = status_code // 100
     if status_class == 5:
+        logging.exception(exception)
         sentry_sdk.capture_exception(exception)
 
     response = encoder(exception_to_dict(exception))